FDTD Computation of Space/Time Integrated Electromagnetic Lagrangian: New Insights into Design of Mutually Coupled Antennas

In this paper, we develop a formalism based on electromagnetic Lagrangian which provides new insights about the near-field reactive energy density around generic antennas for arbitrary spatio-temporal excitation signals. Using electric and magnetic fields calculated via FDTD technique and interpolation routines, we compute the EM Lagrangian density around antennas (thin-wire dipoles and Yagi-Uda Arrays). Spatial maps of time-integrated EM Lagrangian density sheds light onto the capacitive/inductive nature of reactive energy density distribution around antennas and highlight its inherent connection with inter-element mutual coupling.